package org.matheclipse.core.integrate.rubi45;


import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctionCtors.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctions.*;
import org.matheclipse.core.interfaces.IAST;

/** 
 * IndefiniteIntegrationRules from the <a href="http://www.apmaths.uwo.ca/~arich/">Rubi -
 * rule-based integrator</a>.
 *  
 */
public class IntRules16 { 
  public static IAST RULES = List( 
ISetDelayed(Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),n_DEFAULT)),x_Symbol),
    Condition(Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(f,Times(g,x)),n),Cancel(Times(Power(Plus(Times(C1D2,b),Times(c,x)),Times(C2,p)),Power(Power(c,p),-1)))),x),And(And(And(FreeQ(List(a,b,c,d,e,f,g,m,n),x),NonzeroQ(Plus(Times(e,f),Times(CN1,d,g)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),IntegerQ(p)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),CN1D2),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Times(Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),CN1D2),Int(Power(Plus(d,Times(e,x)),m),x)),And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Times(ASymbol,BSymbol,Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(b,Plus(p,C1),Plus(Times(BSymbol,d),Times(CN1,ASymbol,e))),-1)),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),ZeroQ(Plus(m,Times(C2,p),C3))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,c,Plus(p,C1)),-1)),Times(CN1,BSymbol,e,m,Power(Times(C2,c,Plus(p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),RationalQ(m,p)),Less(p,CN1)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(ASymbol,BSymbol,Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(b,Plus(p,C1),Plus(Times(BSymbol,d),Times(CN1,ASymbol,e))),-1)),Times(CN1,ASymbol,BSymbol,e,Plus(m,Times(C2,p),C3),Power(Times(b,Plus(p,C1),Plus(Times(BSymbol,d),Times(CN1,ASymbol,e))),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),RationalQ(p)),Less(p,CN1)),Not(And(RationalQ(m),Greater(m,C0)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(e,Plus(m,C1)),-1)),Times(CN1,BSymbol,Plus(Times(C2,p),C1),Power(Times(e,Plus(m,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),RationalQ(m)),Less(m,CN1)),NonzeroQ(Plus(Times(C2,p),C1))),Or(Not(RationalQ(p)),And(Greater(p,C0),Or(Or(Not(IntegerQ(m)),GreaterEqual(m,Plus(Times(CN2,p),Negate(C2)))),Less(m,Times(CN4,Plus(p,C1))))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(CN2,ASymbol,BSymbol,Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(b,Plus(m,C1),Plus(Times(BSymbol,d),Times(CN1,ASymbol,e))),-1)),Times(BSymbol,Plus(m,Times(C2,p),C3),Power(Times(Plus(m,C1),Plus(Times(BSymbol,d),Times(CN1,ASymbol,e))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),RationalQ(m)),Less(m,CN1)),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),Times(b,m,Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Power(Times(C2,ASymbol,c,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),PositiveIntegerQ(m)),NonzeroQ(Plus(m,Times(C2,p),C2))),Or(Not(RationalQ(p)),Less(m,Plus(Times(C2,p),C2)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(e,Plus(m,Times(C2,p),C2)),-1)),Times(CN1,Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Plus(Times(C2,p),C1),Power(Times(e,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),-1)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),Power(Plus(Times(C2,c,d),Times(CN1,b,e)),-1),Int(Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),x)),Times(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Power(Plus(Times(C2,c,d),Times(CN1,b,e)),-1),Int(Times(Plus(b,Times(C2,c,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Plus(d,Times(e,x)),-1)),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),NonzeroQ(Plus(Times(C2,c,d),Times(CN1,b,e)))),RationalQ(p)),Less(p,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(e,-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x)),Times(BSymbol,Power(e,-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),Or(And(ZeroQ(Plus(m,Times(C2,p),C2)),NonzeroQ(Plus(m,C1))),And(ZeroQ(Plus(Times(C2,c,d),Times(CN1,b,e))),NonzeroQ(Plus(m,Negate(C1)))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),Power(Plus(Times(C2,c,d),Times(CN1,b,e)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x)),Times(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Power(Plus(Times(C2,c,d),Times(CN1,b,e)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Plus(b,Times(C2,c,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),NonzeroQ(Plus(Times(C2,c,d),Times(CN1,b,e)))),ZeroQ(Plus(m,Times(C2,p),C3))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(b,Times(C2,c,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(e,Plus(m,C1),Plus(Times(C2,c,d),Times(CN1,b,e))),-1)),Times(Plus(Times(C2,ASymbol,c,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,Plus(Times(C2,c,d,Plus(Times(C2,p),C1)),Times(b,e,Plus(m,C1))))),Power(Times(e,Plus(m,C1),Plus(Times(C2,c,d),Times(CN1,b,e))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),NonzeroQ(Plus(Times(C2,c,d),Times(CN1,b,e)))),NonzeroQ(Plus(m,Times(C2,p),C2))),NonzeroQ(Plus(m,Times(C2,p),C3))),RationalQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(b,Times(C2,c,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(C2,c,e,Plus(m,Times(C2,p),C2)),-1)),Times(Plus(Times(C2,ASymbol,c,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,Plus(Times(b,e,Plus(m,C1)),Times(C2,c,Plus(d,Times(C2,d,p)))))),Power(Times(C2,c,e,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Not(IntegerQ(p))),NonzeroQ(Plus(Times(C2,c,d),Times(CN1,b,e)))),NonzeroQ(Plus(m,Times(C2,p),C2))),NonzeroQ(Plus(m,Times(C2,p),C3))),Not(And(RationalQ(m),Less(m,CN1)))))),
ISetDelayed(Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_),Power(Plus(f_DEFAULT,Times(g_DEFAULT,x_)),n_)),x_Symbol),
    Condition(Times(Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Power(Plus(Times(C1D2,b),Times(c,x)),Times(C2,p)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(f,Times(g,x)),n),Power(Plus(Times(C1D2,b),Times(c,x)),Times(C2,p))),x)),And(And(And(FreeQ(List(a,b,c,d,e,f,g,m,n),x),NonzeroQ(Plus(Times(e,f),Times(CN1,d,g)))),ZeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),Not(IntegerQ(p))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),ZeroQ(Plus(Times(m,Plus(Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e))),Times(ASymbol,c,e))),Times(CN1,e,Plus(p,C1),Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),ZeroQ(Plus(Times(m,Plus(Times(BSymbol,d),Times(ASymbol,e))),Times(C2,ASymbol,e,Plus(p,C1))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Plus(Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e))),Times(ASymbol,c,e)),Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(p,C1),Plus(Times(C2,c,d),Times(CN1,b,e))),-1)),Times(CN1,e,Plus(Times(m,Plus(Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e))),Times(ASymbol,c,e))),Times(CN1,e,Plus(p,C1),Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Power(Times(c,Plus(p,C1),Plus(Times(C2,c,d),Times(CN1,b,e))),-1),Int(Times(Power(Plus(d,Times(e,x)),Simplify(Plus(m,Negate(C1)))),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Simplify(Plus(p,C1)))),x))),And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),SumSimplerQ(m,CN1)),SumSimplerQ(p,C1)),NonzeroQ(Plus(p,C1))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Plus(Times(BSymbol,d),Times(ASymbol,e)),Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,c,d,Plus(p,C1)),-1)),Times(CN1,e,Plus(Times(m,Plus(Times(BSymbol,d),Times(ASymbol,e))),Times(C2,ASymbol,e,Plus(p,C1))),Power(Times(C2,c,d,Plus(p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Simplify(Plus(m,Negate(C1)))),Power(Plus(a,Times(c,Sqr(x))),Simplify(Plus(p,C1)))),x))),And(And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),SumSimplerQ(m,CN1)),SumSimplerQ(p,C1)),NonzeroQ(Plus(p,C1))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(Plus(Times(C2,c,d),Times(CN1,b,e)),Plus(m,p,C1)),-1)),Times(Plus(Times(m,Plus(Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e))),Times(ASymbol,c,e))),Times(CN1,e,Plus(p,C1),Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Power(Times(e,Plus(Times(C2,c,d),Times(CN1,b,e)),Plus(m,p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),Or(And(And(RationalQ(m),Less(m,CN1)),NonzeroQ(Plus(m,p))),ZeroQ(Plus(m,Times(C2,p),C2)))),NonzeroQ(Plus(m,p,C1))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,c,d,Plus(m,p,C1)),-1)),Times(Plus(Times(m,Plus(Times(BSymbol,c,d),Times(ASymbol,c,e))),Times(C2,e,ASymbol,c,Plus(p,C1))),Power(Times(e,C2,c,d,Plus(m,p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(c,Sqr(x))),p)),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),Or(And(And(RationalQ(m),Less(m,CN1)),NonzeroQ(Plus(m,p))),ZeroQ(Plus(m,Times(C2,p),C2)))),NonzeroQ(Plus(m,p,C1))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),Times(Plus(Times(m,Plus(Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e))),Times(ASymbol,c,e))),Times(CN1,e,Plus(p,C1),Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))),Power(Times(c,e,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),Times(Plus(Times(m,Plus(Times(BSymbol,d),Times(ASymbol,e))),Times(C2,ASymbol,e,Plus(p,C1))),Power(Times(e,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),p)),x))),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),ZeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Int(ExpandIntegrand(Times(Power(Plus(d,Times(e,x)),m),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1)),x),x),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),IntegerQ(m)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Int(ExpandIntegrand(Times(Power(Plus(d,Times(e,x)),m),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(c,Sqr(x))),-1)),x),x),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),IntegerQ(m)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Times(c,m),-1)),Times(Power(c,-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(ASymbol,c,d),Times(CN1,a,BSymbol,e),Times(Plus(Times(BSymbol,c,d),Times(CN1,b,BSymbol,e),Times(ASymbol,c,e)),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),FractionQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Times(c,m),-1)),Times(Power(c,-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(ASymbol,c,d),Times(CN1,a,BSymbol,e),Times(Plus(Times(BSymbol,c,d),Times(ASymbol,c,e)),x)),x),Power(Plus(a,Times(c,Sqr(x))),-1)),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),FractionQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),Sqrt(Plus(d_DEFAULT,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Times(C2,Subst(Int(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d),Times(BSymbol,Sqr(x))),Power(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)),Times(CN1,Plus(Times(C2,c,d),Times(CN1,b,e)),Sqr(x)),Times(c,Power(x,4))),-1)),x),x,Sqrt(Plus(d,Times(e,x))))),And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Plus(a_,Times(c_DEFAULT,Sqr(x_))),Sqrt(Plus(d_DEFAULT,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Times(C2,Subst(Int(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d),Times(BSymbol,Sqr(x))),Power(Plus(Times(c,Sqr(d)),Times(a,Sqr(e)),Times(CN1,C2,c,d,Sqr(x)),Times(c,Power(x,4))),-1)),x),x,Sqrt(Plus(d,Times(e,x))))),And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Times(Plus(m,C1),Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)))),-1)),Times(Power(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Simp(Plus(Times(ASymbol,c,d),Times(CN1,ASymbol,b,e),Times(a,BSymbol,e),Times(CN1,c,Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),FractionQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Times(Plus(m,C1),Plus(Times(c,Sqr(d)),Times(a,Sqr(e)))),-1)),Times(Power(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Simp(Plus(Times(ASymbol,c,d),Times(a,BSymbol,e),Times(CN1,c,Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),x)),x),Power(Plus(a,Times(c,Sqr(x))),-1)),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),FractionQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1),Power(Times(e_DEFAULT,x_),m_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Int(Times(Power(Times(e,x),m),Power(Plus(a,Times(c,Sqr(x))),-1)),x)),Times(BSymbol,Power(e,-1),Int(Times(Power(Times(e,x),Plus(m,C1)),Power(Plus(a,Times(c,Sqr(x))),-1)),x))),And(FreeQ(List(a,c,e,ASymbol,BSymbol),x),Not(RationalQ(m))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(Plus(d,Times(e,x)),m),Times(Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),-1)),x),x),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),Not(RationalQ(m))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),-1),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Int(ExpandIntegrand(Power(Plus(d,Times(e,x)),m),Times(Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(c,Sqr(x))),-1)),x),x),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),Not(RationalQ(m))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_)))),Sqrt(Times(e_DEFAULT,x_))),-1)),x_Symbol),
    Condition(Times(ASymbol,Sqrt(Plus(C1,Times(BSymbol,x,Power(ASymbol,-1)))),Sqrt(Simp(Plus(C1,Times(BSymbol,c,x,Power(Plus(Times(b,BSymbol),Times(CN1,ASymbol,c)),-1))),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),CN1D2),Int(Times(Sqrt(Plus(C1,Times(BSymbol,x,Power(ASymbol,-1)))),Power(Times(Sqrt(Times(e,x)),Sqrt(Simp(Plus(C1,Times(BSymbol,c,x,Power(Plus(Times(b,BSymbol),Times(CN1,ASymbol,c)),-1))),x))),-1)),x)),And(And(FreeQ(List(a,b,c,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),ZeroQ(Plus(Times(ASymbol,b,BSymbol),Times(CN1,a,Sqr(BSymbol)),Times(CN1,Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(c_DEFAULT,Sqr(x_)))),Sqrt(Times(e_DEFAULT,x_))),-1)),x_Symbol),
    Condition(Times(ASymbol,Sqrt(Times(Plus(Sqr(ASymbol),Times(CN1,Sqr(BSymbol),Sqr(x))),Power(ASymbol,-2))),Power(Plus(a,Times(c,Sqr(x))),CN1D2),Int(Times(Sqrt(Plus(C1,Times(BSymbol,x,Power(ASymbol,-1)))),Power(Times(Sqrt(Times(e,x)),Sqrt(Plus(C1,Times(CN1,BSymbol,x,Power(ASymbol,-1))))),-1)),x)),And(FreeQ(List(a,c,e,ASymbol,BSymbol),x),ZeroQ(Plus(Times(a,Sqr(BSymbol)),Times(Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_)))),Sqrt(Plus(d_,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Times(CN1,Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Sqrt(Times(CN1,e,Plus(ASymbol,Times(BSymbol,x)),Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1))),Sqrt(Times(CN1,e,Simp(Plus(Times(b,BSymbol),Times(CN1,ASymbol,c),Times(BSymbol,c,x)),x),Power(Plus(Times(ASymbol,c,e),Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e)))),-1))),Power(Times(e,Sqrt(Plus(a,Times(b,x),Times(c,Sqr(x))))),-1),Int(Times(Sqrt(Simp(Plus(Times(CN1,ASymbol,e,Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1)),Times(CN1,BSymbol,e,x,Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1))),x)),Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Simp(Plus(Times(CN1,e,Plus(Times(b,BSymbol),Times(CN1,ASymbol,c)),Power(Plus(Times(ASymbol,c,e),Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e)))),-1)),Times(CN1,BSymbol,c,e,x,Power(Plus(Times(ASymbol,c,e),Times(BSymbol,Plus(Times(c,d),Times(CN1,b,e)))),-1))),x))),-1)),x)),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),ZeroQ(Plus(Times(ASymbol,b,BSymbol),Times(CN1,a,Sqr(BSymbol)),Times(CN1,Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(c_DEFAULT,Sqr(x_)))),Sqrt(Plus(d_,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Times(CN1,Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Sqrt(Times(CN1,e,Plus(ASymbol,Times(BSymbol,x)),Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1))),Sqrt(Times(e,Plus(ASymbol,Times(CN1,BSymbol,x)),Power(Plus(Times(ASymbol,e),Times(BSymbol,d)),-1))),Power(Times(e,Sqrt(Plus(a,Times(c,Sqr(x))))),-1),Int(Times(Sqrt(Simp(Plus(Times(CN1,ASymbol,e,Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1)),Times(CN1,BSymbol,e,x,Power(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),-1))),x)),Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Simp(Plus(Times(ASymbol,e,Power(Plus(Times(ASymbol,e),Times(BSymbol,d)),-1)),Times(CN1,BSymbol,e,x,Power(Plus(Times(ASymbol,e),Times(BSymbol,d)),-1))),x))),-1)),x)),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),ZeroQ(Plus(Times(a,Sqr(BSymbol)),Times(Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(d_DEFAULT,Times(e_DEFAULT,x_))),Sqrt(Plus(Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))))),-1)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(b,BSymbol),Times(CN1,ASymbol,c)),Power(c,-1),Int(Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Plus(Times(b,x),Times(c,Sqr(x))))),-1),x)),Times(BSymbol,Power(c,-1),Int(Times(Sqrt(Plus(Times(b,x),Times(c,Sqr(x)))),Power(Times(x,Sqrt(Plus(d,Times(e,x)))),-1)),x))),And(And(And(FreeQ(List(b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,d),Times(CN1,b,e)))),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,ASymbol,c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_)))),Sqrt(Plus(d_DEFAULT,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(C2,ASymbol,c),Times(CN1,BSymbol,Plus(b,Negate(Rt(Plus(Sqr(b),Times(CN1,C4,a,c)),C2))))),Power(Times(C2,c),-1),Int(Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Plus(a,Times(b,x),Times(c,Sqr(x))))),-1),x)),Times(BSymbol,Power(Times(C2,c),-1),Int(Times(Plus(b,Negate(Rt(Plus(Sqr(b),Times(CN1,C4,a,c)),C2)),Times(C2,c,x)),Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Plus(a,Times(b,x),Times(c,Sqr(x))))),-1)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),NonzeroQ(Plus(Times(ASymbol,b,BSymbol),Times(CN1,a,Sqr(BSymbol)),Times(CN1,Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(c_DEFAULT,Sqr(x_)))),Sqrt(Times(e_DEFAULT,x_))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,c),Times(BSymbol,Rt(Times(CN1,a,c),C2))),Power(Times(c,Sqrt(Plus(a,Times(c,Sqr(x))))),-1),Sqrt(Times(Plus(a,Times(c,Sqr(x))),Power(a,-1))),Int(Power(Times(Sqrt(Times(e,x)),Sqrt(Plus(C1,Times(CN1,c,x,Power(Rt(Times(CN1,a,c),C2),-1)))),Sqrt(Plus(C1,Times(c,x,Power(Rt(Times(CN1,a,c),C2),-1))))),-1),x)),Times(CN1,BSymbol,Power(c,-1),Int(Times(Plus(Rt(Times(CN1,a,c),C2),Times(CN1,c,x)),Power(Times(Sqrt(Times(e,x)),Sqrt(Plus(a,Times(c,Sqr(x))))),-1)),x))),And(FreeQ(List(a,c,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(a,Sqr(BSymbol)),Times(Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Times(Sqrt(Plus(a_,Times(c_DEFAULT,Sqr(x_)))),Sqrt(Plus(d_DEFAULT,Times(e_DEFAULT,x_)))),-1)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,c),Times(BSymbol,Rt(Times(CN1,a,c),C2))),Power(c,-1),Int(Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Plus(a,Times(c,Sqr(x))))),-1),x)),Times(CN1,BSymbol,Power(c,-1),Int(Times(Plus(Rt(Times(CN1,a,c),C2),Times(CN1,c,x)),Power(Times(Sqrt(Plus(d,Times(e,x))),Sqrt(Plus(a,Times(c,Sqr(x))))),-1)),x))),And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),NonzeroQ(Plus(Times(a,Sqr(BSymbol)),Times(Sqr(ASymbol),c)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Times(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),Sqrt(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))))),-1)),x_Symbol),
    Condition(Times(C4,ASymbol,Plus(a,Negate(d)),Power(Plus(Times(b,d),Times(CN1,a,e)),-1),Subst(Int(Power(Plus(Times(C4,Plus(a,Negate(d))),Negate(Sqr(x))),-1),x),x,Times(Plus(Times(C2,Plus(a,Negate(d))),Times(Plus(b,Negate(e)),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),CN1D2)))),And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),ZeroQ(Plus(Times(C4,c,Plus(a,Negate(d))),Negate(Sqr(Plus(b,Negate(e))))))),ZeroQ(Plus(Times(ASymbol,e,Plus(b,Negate(e))),Times(CN1,C2,BSymbol,Plus(Times(b,d),Times(CN1,a,e)))))),NonzeroQ(Plus(Times(b,d),Times(CN1,a,e)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(e,-1),Int(Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),x)),Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(e,-1),Int(Times(Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Plus(d,Times(e,x)),-1)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(p)),Less(Less(CN1,p),C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),-1)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(e,-1),Int(Power(Plus(a,Times(c,Sqr(x))),p),x)),Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(e,-1),Int(Times(Power(Plus(a,Times(c,Sqr(x))),p),Power(Plus(d,Times(e,x)),-1)),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),RationalQ(p)),Less(Less(CN1,p),C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(Plus(m,C1),Plus(Times(c,Sqr(d)),Times(a,Sqr(e)))),-1)),And(And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),ZeroQ(Plus(Times(ASymbol,c,d),Times(a,BSymbol,e)))),ZeroQ(Plus(m,Times(C2,p),C3))),NonzeroQ(Plus(m,C1))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Int(ExpandIntegrand(Times(Power(Plus(d,Times(e,x)),m),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x),x),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),PositiveIntegerQ(p)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Int(ExpandIntegrand(Times(Power(Plus(d,Times(e,x)),m),Plus(ASymbol,Times(BSymbol,x)),Power(Plus(a,Times(c,Sqr(x))),p)),x),x),And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),PositiveIntegerQ(p)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,d,Plus(Times(C2,p),C1)),Times(e,BSymbol,Plus(m,C1),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(Sqr(e),Plus(m,C1),Plus(m,Times(C2,p),C2)),-1)),Times(p,Power(Times(Sqr(e),Plus(m,C1),Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Simp(Plus(Times(BSymbol,Plus(Times(b,d),Times(C2,a,e),Times(C2,a,e,m),Times(C2,b,d,p))),Times(CN1,ASymbol,b,e,Plus(m,Times(C2,p),C2)),Times(Plus(Times(BSymbol,Plus(Times(C2,c,d),Times(b,e),Times(b,e,m),Times(C4,c,d,p))),Times(CN1,C2,ASymbol,c,e,Plus(m,Times(C2,p),C2))),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,Negate(C1)))),x))),And(And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(p)),Greater(p,C0)),Or(Or(And(RationalQ(m),Less(m,CN1)),Equal(p,C1)),And(IntegerQ(p),Not(RationalQ(m))))),NonzeroQ(Plus(m,C1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,d,Plus(Times(C2,p),C1)),Times(e,BSymbol,Plus(m,C1),x)),Power(Plus(a,Times(c,Sqr(x))),p),Power(Times(Sqr(e),Plus(m,C1),Plus(m,Times(C2,p),C2)),-1)),Times(p,Power(Times(Sqr(e),Plus(m,C1),Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Simp(Plus(Times(BSymbol,Plus(Times(C2,a,e),Times(C2,a,e,m))),Times(Plus(Times(BSymbol,Plus(Times(C2,c,d),Times(C4,c,d,p))),Times(CN1,C2,ASymbol,c,e,Plus(m,Times(C2,p),C2))),x)),x),Power(Plus(a,Times(c,Sqr(x))),Plus(p,Negate(C1)))),x))),And(And(And(And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),RationalQ(p)),Greater(p,C0)),Or(Or(And(RationalQ(m),Less(m,CN1)),Equal(p,C1)),And(IntegerQ(p),Not(RationalQ(m))))),NonzeroQ(Plus(m,C1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,c,Plus(p,C1)),-1)),Times(CN1,BSymbol,e,m,Power(Times(C2,c,Plus(p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(m,p)),Greater(m,C0)),Less(p,CN1)),ZeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),m),Plus(Times(ASymbol,b),Times(CN1,C2,a,BSymbol),Times(CN1,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(Plus(p,C1),Plus(Sqr(b),Times(CN1,C4,a,c))),-1)),Times(Power(Times(Plus(p,C1),Plus(Sqr(b),Times(CN1,C4,a,c))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(BSymbol,Plus(Times(C2,a,e,m),Times(b,d,Plus(Times(C2,p),C3)))),Times(CN1,ASymbol,Plus(Times(b,e,m),Times(C2,c,d,Plus(Times(C2,p),C3)))),Times(e,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),Plus(m,Times(C2,p),C3),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(m,p)),Less(p,CN1)),Greater(m,C0)),NonzeroQ(Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),m),Plus(Times(a,BSymbol),Times(CN1,c,ASymbol,x)),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,a,c,Plus(p,C1)),-1)),Times(CN1,Power(Times(C2,a,c,Plus(p,C1)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(a,e,BSymbol,m),Times(CN1,c,d,ASymbol,Plus(Times(C2,p),C3)),Times(CN1,c,e,ASymbol,Plus(m,Times(C2,p),C3),x)),x),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),RationalQ(m,p)),Less(p,CN1)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,c,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,Plus(Times(c,d),Times(C2,c,d,p),Times(CN1,b,e,p))),Times(BSymbol,c,e,Plus(m,Times(C2,p),C1),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p),Power(Times(c,Sqr(e),Plus(m,Times(C2,p),C1),Plus(m,Times(C2,p),C2)),-1)),Times(CN1,p,Power(Times(c,Sqr(e),Plus(m,Times(C2,p),C1),Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Simp(Plus(Times(ASymbol,c,e,Plus(Times(b,d),Times(CN1,C2,a,e)),Plus(m,Times(C2,p),C2)),Times(BSymbol,Plus(Times(a,e,Plus(Times(b,e),Times(CN1,C2,c,d,m),Times(b,e,m))),Times(b,d,Plus(Times(b,e,p),Times(CN1,c,d),Times(CN1,C2,c,d,p))))),Times(Plus(Times(ASymbol,c,e,Plus(Times(C2,c,d),Times(CN1,b,e)),Plus(m,Times(C2,p),C2)),Times(BSymbol,Plus(Times(Sqr(b),Sqr(e),Plus(p,m,C1)),Times(CN1,C2,Sqr(c),Sqr(d),Plus(C1,Times(C2,p))),Times(CN1,c,e,Plus(Times(b,d,Plus(m,Times(CN1,C2,p))),Times(C2,a,e,Plus(m,Times(C2,p),C1))))))),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,Negate(C1)))),x))),And(And(And(And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(p)),Greater(p,C0)),Or(Or(IntegerQ(p),Not(RationalQ(m))),And(LessEqual(CN1,m),Less(m,C0)))),NonzeroQ(Plus(m,Times(C2,p),C1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,c,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,c,d,Plus(Times(C2,p),C1)),Times(BSymbol,c,e,Plus(m,Times(C2,p),C1),x)),Power(Plus(a,Times(c,Sqr(x))),p),Power(Times(c,Sqr(e),Plus(m,Times(C2,p),C1),Plus(m,Times(C2,p),C2)),-1)),Times(C2,p,Power(Times(c,Sqr(e),Plus(m,Times(C2,p),C1),Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Simp(Plus(Times(ASymbol,a,c,Sqr(e),Plus(m,Times(C2,p),C2)),Times(BSymbol,a,c,d,e,m),Times(CN1,Plus(Times(ASymbol,Sqr(c),d,e,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,Plus(Times(Sqr(c),Sqr(d),Plus(Times(C2,p),C1)),Times(a,c,Sqr(e),Plus(m,Times(C2,p),C1))))),x)),x),Power(Plus(a,Times(c,Sqr(x))),Plus(p,Negate(C1)))),x))),And(And(And(And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),RationalQ(p)),Greater(p,C0)),Or(Or(IntegerQ(p),Not(RationalQ(m))),And(LessEqual(CN1,m),Less(m,C0)))),NonzeroQ(Plus(m,Times(C2,p),C1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,Plus(Times(b,c,d),Times(CN1,Sqr(b),e),Times(C2,a,c,e))),Times(CN1,a,BSymbol,Plus(Times(C2,c,d),Times(CN1,b,e))),Times(c,Plus(Times(ASymbol,Plus(Times(C2,c,d),Times(CN1,b,e))),Times(CN1,BSymbol,Plus(Times(b,d),Times(CN1,C2,a,e)))),x)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(Plus(p,C1),Plus(Sqr(b),Times(CN1,C4,a,c)),Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)))),-1)),Times(Power(Times(Plus(p,C1),Plus(Sqr(b),Times(CN1,C4,a,c)),Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)))),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Simp(Plus(Times(ASymbol,Plus(Times(b,c,d,e,Plus(Times(C2,p),Negate(m),C2)),Times(Sqr(b),Sqr(e),Plus(p,m,C2)),Times(CN1,C2,Sqr(c),Sqr(d),Plus(Times(C2,p),C3)),Times(CN1,C2,a,c,Sqr(e),Plus(m,Times(C2,p),C3)))),Times(CN1,BSymbol,Plus(Times(a,e,Plus(Times(b,e),Times(CN1,C2,c,d,m),Times(b,e,m))),Times(b,d,Plus(Times(CN3,c,d),Times(b,e),Times(CN1,C2,c,d,p),Times(b,e,p))))),Times(c,e,Plus(Times(BSymbol,Plus(Times(b,d),Times(CN1,C2,a,e))),Times(CN1,ASymbol,Plus(Times(C2,c,d),Times(CN1,b,e)))),Plus(m,Times(C2,p),C4),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),RationalQ(p)),Less(p,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(CN1,Power(Plus(d,Times(e,x)),Plus(m,C1)),Plus(Times(ASymbol,a,c,e),Times(CN1,a,BSymbol,c,d),Times(c,Plus(Times(ASymbol,c,d),Times(BSymbol,a,e)),x)),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(C2,a,c,Plus(p,C1),Plus(Times(c,Sqr(d)),Times(a,Sqr(e)))),-1)),Times(Power(Times(C2,a,c,Plus(p,C1),Plus(Times(c,Sqr(d)),Times(a,Sqr(e)))),-1),Int(Times(Power(Plus(d,Times(e,x)),m),Simp(Plus(Times(ASymbol,Plus(Times(Sqr(c),Sqr(d),Plus(Times(C2,p),C3)),Times(a,c,Sqr(e),Plus(m,Times(C2,p),C3)))),Times(CN1,BSymbol,a,e,c,d,m),Times(c,e,Plus(Times(BSymbol,a,e),Times(ASymbol,c,d)),Plus(m,Times(C2,p),C4),x)),x),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1))),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),RationalQ(p)),Less(p,CN1)))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),Times(Power(Times(c,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(m,Plus(Times(ASymbol,c,d),Times(CN1,a,BSymbol,e))),Times(CN1,d,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),Plus(p,C1)),Times(Plus(Times(Plus(Times(BSymbol,c,d),Times(CN1,b,BSymbol,e),Times(ASymbol,c,e)),m),Times(CN1,e,Plus(Times(b,BSymbol),Times(CN1,C2,ASymbol,c)),Plus(p,C1))),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),If(RationalQ(m),Greater(m,C0),SumSimplerQ(m,CN1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_,Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(Plus(d,Times(e,x)),m),Power(Plus(a,Times(c,Sqr(x))),Plus(p,C1)),Power(Times(c,Plus(m,Times(C2,p),C2)),-1)),Times(Power(Times(c,Plus(m,Times(C2,p),C2)),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,Negate(C1))),Simp(Plus(Times(c,d,ASymbol,Plus(m,Times(C2,p),C2)),Times(CN1,BSymbol,a,e,m),Times(c,Plus(Times(e,ASymbol,Plus(m,Times(C2,p),C2)),Times(BSymbol,d,m)),x)),x),Power(Plus(a,Times(c,Sqr(x))),p)),x))),And(And(And(And(FreeQ(List(a,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(a,Sqr(e))))),If(RationalQ(m),Greater(m,C0),SumSimplerQ(m,CN1))),NonzeroQ(Plus(m,Times(C2,p),C2))))),
ISetDelayed(Int(Times(Plus(A_DEFAULT,Times(B_DEFAULT,x_)),Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT),Power(Plus(d_DEFAULT,Times(e_DEFAULT,x_)),m_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Power(Plus(d,Times(e,x)),Plus(m,C1)),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),Plus(p,C1)),Power(Times(Plus(m,C1),Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)))),-1)),Times(Power(Times(Plus(m,C1),Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e)))),-1),Int(Times(Power(Plus(d,Times(e,x)),Plus(m,C1)),Simp(Plus(Times(Plus(Times(ASymbol,c,d),Times(CN1,ASymbol,b,e),Times(a,BSymbol,e)),Plus(m,C1)),Times(b,Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)),Plus(p,C1)),Times(CN1,c,Plus(Times(ASymbol,e),Times(CN1,BSymbol,d)),Plus(m,Times(C2,p),C3),x)),x),Power(Plus(a,Times(b,x),Times(c,Sqr(x))),p)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,ASymbol,BSymbol,m,p),x),NonzeroQ(Plus(Times(BSymbol,d),Times(CN1,ASymbol,e)))),NonzeroQ(Plus(Sqr(b),Times(CN1,C4,a,c)))),NonzeroQ(Plus(Times(c,Sqr(d)),Times(CN1,b,d,e),Times(a,Sqr(e))))),If(RationalQ(m),Less(m,CN1),And(NonzeroQ(Plus(m,C1)),SumSimplerQ(m,C1))))))
  );
}
